Johanna Konta showed plenty of skill and grit to beat Timea Babos in the US Open first round at Flushing Meadows. Photograph: John G. Mabanglo/Epa

As tempting as it is to embrace a new British tennis hope, Johanna Konta, the latest sporting acquisition from south of the equator, has at least one attribute needed to succeed at the highest level: character.

When she goes into her second-round match against the 6ft Belarussian Olga Govortsova on Thursday, the Sydney-born import with the Hungarian parents and Australian attitude will be comforted by the very recent evidence that she can dig herself out of the most awful holes.

Having won the first set against Timea Babos, her sometime doubles partner (and a bona fide Hungarian), in the first round on Tuesday, Konta had to come from 5-1 down in the second set, enduring a mind-sapping 14 deuce points in the ninth game, to win what could prove to be a breakthrough match for her.

Yet she seemed wholly relaxed about it afterwards. "I haven't really kept time on other games," she said when asked was it the longest of her career, "but it was definitely a long one. I don't even know how many deuces."

She does now. And so do her peers. Anyone who can survive the fire of such an examination is a player to be feared. Whether Govortsova in her fifth US Open will be unduly worried we will soon discover. This is Konta's first visit to Flushing Meadows – but you might not know it from the newly minted British player's demeanour. Konta, 21, has lived in Eastbourne with her immigrant parents since she was 14, and has the air of someone with a hinterland wider than a mere tennis court. She also talks with the authority of an athlete who is comfortable in the company of quality opponents – and British rivals.

Konta says she has been welcomed by the small but quality band of British players jostling alongside each other in the top 100 and hopes to catch the eye of Judy Murray to earn a place in the Fed Cup team.

"I wouldn't say we're like unbelievably close," she says of Laura Robson, Heather Watson, Anne Keothavong and Elena Baltacha, "just because of the nature of our sport. But we definitely are friends. We practice together, go out to dinner some times."

The rankings suggest Govortsova, a clay‑court specialist who hugs the baseline and works opponents over with a metronomic backhand and is at 67 in the world, will have the edge on Konta, who lurks at 203 on the WTA list but will leap a massive 54 places if she reaches the third round.

That would be quite a feat – and it would excite considerable interest in a player whose profile has hitherto relied on the quirk of qualifying as British after several years of queueing at the Home Office.

"That was a very, very long process," she said. "There were so many questions being asked. It was something that I wanted out of the way because I very much wanted GBR next to my name for a very long time. To finally have it is just a pure weight off my shoulders.

"No one believed that I was definitely getting it. There were a lot of doubts. Not many people understood the situation, but I always knew I was going to get it. I don't know what it is to feel very British. But I feel that it's home. So I'm very happy to represent Great Britain.

"I got to the UK in 2005. It wasn't straight away a decision of: 'OK, now I'm going to become British.' It gradually became a process after spending some time there, getting to know the people who are involved in the [Lawn Tennis Association]. Also, after I was doing reasonably well in juniors, there became more interest, the fact that I wasn't living in Australia any more. That all nudged things in that direction."

Having been nudged, she duly delivered. Her game is uncomplicated, unspectacular even, but solid. Asked to define her strengths, she kept it simple: "I think I'm a good athlete. I guess I have a reasonable physique for the sport I do."

Govortsova will be the favourite on Thursday, and she will know that, whatever her calmness in a press conference, stepping on to a bigger stage at a slam will test the nerves of her more inexperienced opponent. Nevertheless, someone who lists her career highlight as winning the Wimbledon junior doubles (with Vika Azarenka) eight years ago may just be there for the taking. There have been bigger upsets at this tournament.